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Hi everyone, it's me, Mr C, for our second position and direction maths lesson for year four.

So let's take a little look, shall we.

Make sure you've done our knowledge quiz to start off with so that you're ready to move on to today's learning and to find out our amazing fact.

Welcome back everyone.

So, shall we take a look? Here's a magical maths fact that I find utterly fascinating.

And I was just thinking, because I've spent a lot of time dreaming of travelling over the last few weeks, but not actually being able to do so.

Just thinking about places I've been to and the distance between different places.

Then I was thinking about the size of the UK, where we live, compared to other countries.

And did you know that if you took the United Kingdom and kind of use it like a jigsaw piece and multiplied it loads of times to put it together, you could fit about 40 lots of the United Kingdom inside the space taken up by the USA.

Similarly to that, the UK could fit into Russia about 70 times and it would take about 120 versions of the United Kingdom to fill Africa.

It's absolutely mind blowing.

It makes you realise just how big some countries are.

It takes long enough for me to get to work every day.

Now, thinking about the tiny amounts of the UK that that takes up and thinking about expanding it bigger and bigger and bigger and bigger and bigger, crazy to think just how big some countries or continents actually are.

I thought that was quite an interesting little fact to share with you.

So, let's have a look for today, shall we? And you're going to need your usual stuff, your pencil, your ruler, something to work on and somewhere quiet with no distractions.

Now, today, this is what we're going to be doing, and some of what we already have done.

We've done our knowledge quiz already and we're about to pop and do our key learning and key vocabulary.

After that, we're going to do our number trees warmup, which I'm really enjoying.

I love putting these together 'cause I like working them out while I make them for you.

Then we're going to recap on coordinates and how we can link a set of coordinates to shapes.

And then our main activities are coordinates of vertices investigation.

It's quite a tricky one that might just take some slow progress.

I'm going to say now, stick with it, be resilient because it's worth it.

And then a final knowledge quiz to see what you've remembered.

So, our key learning today is to investigate a problem describing position on a 2-D grid as coordinates.

So our vocabulary is much the same as yesterday.

2-D, grid, X axis, Y axis, axes, plot, vertices, origin, and coordinates.

Fantastic.

Bear those words in mind 'cause we're going to be using them quite a lot today.

So, here is your starting warmup.

You know the routine by now, we're looking at filling in the missing numbers from our magic trees and number trees.

Remember, the two digits underneath add together to give the number on top.

So four add something gives me 13, five out add something gives me 14.

Until we get to our target number now for two trees today, you've got our final number, the two trees you've got to work it out.

Best of luck folks.

I know you can do it, go for it.

How was that then? Did you manage that okay? Did you manage to fill in those missing numbers on your number trees? I'm sure you did.

So, I think what we should do now then is just have a look at those answers, don't you? So here they are.

Take a look.

Remember, we're adding these two together to give us this one.

How did you do? Just spend some time checking over your answers and seeing how you did.

I think I want to try one more time with these and I'm going to try and give you the smallest number of numbers, the smallest number of numbers, yeah that work, the smallest number of numbers in each tree to see how well you can calculate those missing values.

Because I think you're pretty much experts with this now.

Brilliant! Okay, shall we move along? I think we probably should.

So let's just recap on what coordinates are.

Remember, a coordinate is a way of showing the position of something on a grid.

Okay, and just like pirates, we can use them where X marks the spot, people with maps would use them.

We would show where something is by naming the place using coordinates.

And remember, we do that on a grid with two sets of axes, the X axis, which goes across, the horizontal one, remember that, the X axis? Looks like a cross, goes across, it's horizontal.

The Y axis, Y has a tail, it drops down.

That axis goes down.

So we'd read X and then Y and where those lines cross, we have a value, I mean, could represent that value using coordinates, which are those two numbers inside a set of brackets.

Let's just look further at this again, just to remind ourselves.

So, you've got the grid, remember our X and our Y axis, and remember here where there is no value.

It was still where we started at zero along the rope.

That, remember is called our origin, yeah.

Also, remember when we plot coordinates, it's not in the middle of the square, it's where the lines cross.

Here, see the lines are crossing.

All of these, and I can show it in any way, really.

These are all different coordinates, but they're where the lines cross, okay? So, to recap, along the corridor or go down the stairs.

So to get to this X, I've gone one, two, three, four, five along and one, two, three, up.

Five along, three up, five on the X axis, three on the Y axis.

Then I can show it in brackets.

Five, comma three with the brackets around it.

So let's try this one, shall we? Let's go here.

How many along have I gone? One, two, three, along, and one, two, three, four, five, six, seven, eight, nine up, three along, nine up, surrounded by brackets just to show me where that would be.

It's all very logical, isn't it really? We just got to be very routine about it and that we do our X and then the Y axis.

And then it's just the case of counting.

So take a look here.

What I've done is I've plotted four points.

I've gone two along and nine up.

I've gone five along and eight up.

I've gone five along and four up and two along and three up.

Those are the four corners of the quadrilateral.

When I joined them up, they gave me a trapezium.

It's much similar to our last session where I asked you to plot the points for two different quadrilaterals on each grid.

Well, that's all we've done here.

It's a quadrilateral because it has four sides.

So we've now plotted those four points to create a shape and we've named it.

It's a trapezium.

So, how well do you think you can do that? You've got one, two, three sets of coordinates.

You need to plot those coordinates just a little cross and then try and figure out what shape is in each of those grids.

So let's have a look at this first one here.

I've gone one along, X comes first, and one up, Y comes second.

And mark that point there and then I'll do the same for each of them.

And I should be able to see what kind of quadrilateral shape I've made and I'm going to name it for each.

And that's it! Plot the points, spot the shape, and name it.

When you've done that, come back and join us.

Okay, let's take a look at those answers.

I'm sure you've managed to do that absolutely beautifully.

So shall we take a look? Here are the answers that I came up with when I was out for myself.

So for the first one if you look and plot each of those points and if you want to, you can always do this to remind you where each of those points are.

That's quite a useful little trick to do, actually.

This one is five along, five up.

It just gets you into good habits, really.

One along, five up.

Now I could do that for all of them, but I now know that when I look at this, I've created a square.

Here, I've made an oblong and this one is our rhombus, okay? Brilliant.

Well done.

So, we're going to use that in a moment to help us.

We're looking at the corners, the vertices.

Specifically going to be focusing on squares.

Before we do that though, here, you've got a whole alphabet of points plotted on there.

There are 12 of them altogether.

Can you write the coordinates for each? So, looking at A first, letter A, I'm going to find it on the grid, here it is, point A, how many along, how many up, okay? I've gone two along, ten up.

So I would write it like two along, ten up, like this.

Can you fill in the rest? Okay, well let's take a look then at those answers and see how you did.

Here are our answers.

Just casting your eyes over.

Remember, we're reading the X axis first and then the Y axis.

I'm just going to write it again just to remind us.

X and then Y, always remember that order.

Along the corridors or sometimes down the stairs.

Well done.

Okay.

So this is our main task.

I'm going to explain it to you, but listen really carefully.

'cause it is, it looks tricky.

It isn't, it's just got a lot of words to go with and I've tried to slim the wording down.

Now, and you can see lots of Xs marked on that grid.

Each of those Xs represent a corner, or another vertices of a square.

Okay, and there are eight squares all together on this grid.

There are two colours as well, you'll notice in terms of the crosses.

If it's a red cross, if it's a red X, then that corner is used in two different squares.

So for example, here, this is the corner of one square and also the corner of another square.

But these three are not, it's only the red ones that are the corners of more than one square.

Now, all the squares are different sizes and they don't all just sit in the normal square way.

They might've turned a little bit.

Okay.

Also, just bringing your attention to these axes.

We don't go up in one, this time we're counting in fives, five, 10, 15, 20, axes don't always need to be the same.

Now, I'm not just going to say off you go and do this because it's tricky.

I'm giving you a freebie.

Now, one of the squares is there.

That is one of the squares.

Okay.

And you can see it's not sitting on a square normally would.

Now this one here is shared by another square.

It's the corner of a second square.

Okay.

Some of them are quite obvious.

I can see a square down here somewhere that's quite obvious and I can see a square here that's quite obvious.

So go for the obvious ones first and it may just be a case of using trial and error.

Now, I will say this task can get frustrating, but, don't give up.

Over the last few weeks together, we've gone through lots of tricky sessions and you've always been persistent and you've always been resilient, so keep going with that.

Okay.

If at first it isn't working out, try an alternative way.

If you can't find all the squares, that doesn't matter.

Find the ones you can.

If you find more than eight squares, then you've done some kind of magic.

So just stick, go for the obvious ones first and thinking, okay, I need to remember that any red cross is a corner on two squares.

If you have two squares that use one of the black crosses as a corner, then you know it's a mistake.

Give it a really good go and I'll see you when you're ready.

Guys, how was that? Has it really hurt your head? It was tricky, right? And then eventually, you start going a bit ugh because there are so many crosses to look at, but, I will share with you the solution.

I've also written down all the coordinates for you as well, but you'll see that each of the squares is slightly different, either a different size or sitting in a different way on that grid.

So I'm just going to give you a second to take a look.

If you remember, I'd said to you that some of those squares were really obvious like this one, this was a really clear, obvious square, and I thought this one was as well.

So those were the two that I started with when I did it.

And I tried to find any other squares that was sitting the same way around.

So I found the pink one here was sitting the same way.

And from there, I was able to find my way around the rest.

The one that got me the most, and I don't know why, 'cause it should have been quite simple, was this one here, this pesky little number just kept tricking me And I couldn't quite figure out where it went.

And actually, it's quite obvious when you look at it, 'cause that line had to go here.

So guys, well done if you managed to find those vertices.

It wasn't easy, it was a tricky task, but I wanted to push you because I know how hard you've been working.

So, that then just leaves me with one final thing to say to you and you know what it's going to be.

We've got our final knowledge quiz right here for you to take.

Hop off and do that.

Come back and see me when you're ready.

Welcome back, folks.

Well, we've made it.

That was a tough one, but we survived.

We came out the other side and if you didn't find all of those squares in the investigation, don't worry, you could always go back and have a look and see what, go back and see what other quadrilaterals you can make on that same grid.

Can you find any other different shapes that aren't squares? Very well done.

I'm really proud of you today.

That was a toughie, so double thumbs up, say I, and from me, Mr C, that's it until next time.

So, bye, see you soon.

Take care!.